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Recent questions tagged number-theory
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#numbertheory
Prove that : In triangular series 1 = 1 1+2 = 3 1+2+3 = 6 1+2+3+4 = 10 ………….. Triangular number in 8n+1 always form perfect square .
NarutoUzumaki
asked
in
Mathematical Logic
Oct 6, 2023
by
NarutoUzumaki
163
views
number-theory
discrete-mathematics
4
votes
1
answer
2
GATE IN 2023 | GA Question: 3
A 'frabjous' number is defined as a $3$ digit number with all digits odd, and no two adjacent digits being the same. For example, $137$ is a frabjous number, while $133$ is not. How many such frabjous numbers exist? $125$ $720$ $60$ $80$
admin
asked
in
Quantitative Aptitude
May 22, 2023
by
admin
3.2k
views
gatein-2023
quantitative-aptitude
number-theory
2
votes
1
answer
3
GATE ECE 2023 | GA Question: 3
What is the smallest number with distinct digits whose digits add up to $45?$ $123555789$ $123457869$ $123456789$ $99999$
admin
asked
in
Quantitative Aptitude
May 20, 2023
by
admin
1.7k
views
gateece-2023
quantitative-aptitude
number-theory
1
vote
1
answer
4
TIFR CSE 2021 | Part A | Question: 7
Let $d$ be the positive square integers (that is, it is a square of some integer) that are factors of $20^{5} \times 21^{5}$. Which of the following is true about $d$? $50\leq d< 100$ $100\leq d< 150$ $150\leq d< 200$ $200\leq d< 300$ $300\leq d$
soujanyareddy13
asked
in
Quantitative Aptitude
Mar 25, 2021
by
soujanyareddy13
494
views
tifr2021
quantitative-aptitude
number-theory
5
votes
2
answers
5
GATE Electrical 2021 | GA Question: 4
Which one of the following numbers is exactly divisible by $\left ( 11^{13} +1\right )$? $11^{26} +1$ $11^{33} +1$ $11^{39} -1$ $11^{52} -1$
Arjun
asked
in
Quantitative Aptitude
Feb 19, 2021
by
Arjun
7.1k
views
gateee-2021
quantitative-aptitude
number-system
number-theory
3
votes
2
answers
6
TIFR CSE 2020 | Part A | Question: 15
The sequence $s_{0},s_{1},\dots , s_{9}$ is defined as follows: $s_{0} = s_{1} + 1$ $2s_{i} = s_{i-1} + s_{i+1} + 2 \text{ for } 1 \leq i \leq 8$ $2s_{9} = s_{8} + 2$ What is $s_{0}$? $81$ $95$ $100$ $121$ $190$
admin
asked
in
Quantitative Aptitude
Feb 10, 2020
by
admin
770
views
tifr2020
quantitative-aptitude
number-theory
3
votes
2
answers
7
TIFR CSE 2020 | Part A | Question: 9
A contiguous part, i.e., a set of adjacent sheets, is missing from Tharoor's GRE preparation book. The number on the first missing page is $183$, and it is known that the number on the last missing page has the same three digits, but in a different ... front and one at the back. How many pages are missing from Tharoor's book? $45$ $135$ $136$ $198$ $450$
admin
asked
in
Quantitative Aptitude
Feb 10, 2020
by
admin
865
views
tifr2020
quantitative-aptitude
number-theory
2
votes
1
answer
8
TIFR CSE 2020 | Part A | Question: 6
What is the maximum number of regions that the plane $\mathbb{R}^{2}$ can be partitioned into using $10$ lines? $25$ $50$ $55$ $56$ $1024$ Hint: Let $A(n)$ be the maximum number of partitions that can be made by $n$ lines. Observe that $A(0) = 1, A(2) = 2, A(2) = 4$ etc. Come up with a recurrence equation for $A(n)$.
admin
asked
in
Quantitative Aptitude
Feb 10, 2020
by
admin
807
views
tifr2020
general-aptitude
quantitative-aptitude
number-theory
3
votes
5
answers
9
ISI2018-MMA-3
The number of trailing zeros in $100!$ is $21$ $23$ $24$ $25$
akash.dinkar12
asked
in
Quantitative Aptitude
May 11, 2019
by
akash.dinkar12
957
views
isi2018-mma
general-aptitude
quantitative-aptitude
number-theory
0
votes
2
answers
10
Number theory
Why does a perfect square number have odd number of factors?
Sammohan Ganguly
asked
in
Mathematical Logic
Apr 20, 2018
by
Sammohan Ganguly
433
views
number-theory
1
vote
2
answers
11
Number Theory
A prison houses 100 inmates, one in each of 100 cells, guarded by a total of 100 warders. One evening, all the cells are locked and the keys left in the locks. As the first warder leaves, she turns every key, unlocking all the doors. The second warder ... every third key and so on. Finally the last warder turns the key in just the last cell. Which doors are left unlocked and why?
Mk Utkarsh
asked
in
Numerical Methods
Apr 13, 2018
by
Mk Utkarsh
773
views
number-theory
1
vote
0
answers
12
Self doubt
Why floating point in de-normalized normal form has range between : $\pm1\times2^{-149}$ and $\pm(1 - 2 ^{-23})\times2^{-126}$
Durgesh Singh
asked
in
Digital Logic
Jan 13, 2018
by
Durgesh Singh
557
views
floating-point-representation
number-theory
digital-logic
0
votes
0
answers
13
Kenneth Rosen section 3.4 Exercise question 12
Is this approach right in proving a theorem Ques: show that a mod m = b mod m if a is congruent to b (mod m) Proof: given a is congruent to b(mod m) According to definition: a - b / m i.e a - b = mx (for some integer x). ....(1) Also a = ... by equation (3) then we get a mod m = my + a my + a can also be written as b mod m Therefore, a mod m = b mod m
Jaspreet Singh 4
asked
in
Set Theory & Algebra
Aug 19, 2017
by
Jaspreet Singh 4
388
views
number-theory
2
votes
1
answer
14
Question on Number System
Find the remainder of $\frac{9^{1}+9^{2}+...+9^{n}}{6}$ where $n$ is multiple of 11. I am getting $0$ or $3$. But given answer is 3. Can anyone check?
Aghori
asked
in
Combinatory
Jul 12, 2017
by
Aghori
2.0k
views
number-theory
3
votes
1
answer
15
Question on Number System.
If $N = 1!+2!+3!+...+10!$. What is the last digit of $N^{N}$?
Aghori
asked
in
Combinatory
Jul 12, 2017
by
Aghori
540
views
number-theory
5
votes
1
answer
16
Series Summation
Series summation of $S_n$ in closed form? $\begin{align*} &S_n = \frac{1}{1.2.3.4} + \frac{1}{2.3.4.5} + \frac{1}{3.4.5.6} + \dots + \frac{1}{n.(n+1).(n+2).(n+3)} \end{align*}$
dd
asked
in
Set Theory & Algebra
Jun 11, 2017
by
dd
789
views
number-theory
summation
discrete-mathematics
0
votes
1
answer
17
Divisibility Test of 11
This is the statement for Divisibility test of 11. Add and subtract digits in an alternating pattern (add digit, subtract next digit, add next digit, etc). Then check if that answer is divisible by 11. This is the proof that I found : If x is divisible by 11, then x ≡ 0 (mod ... ------------------------------------- Now, I didn't understand the proof starting from But.
Uzumaki Naruto
asked
in
Mathematical Logic
May 12, 2017
by
Uzumaki Naruto
623
views
number-theory
divisibility
proof
7
votes
1
answer
18
ISI2004-MIII: 11
If $\alpha 1,\alpha 2,\dots,\alpha n$ are the positive numbers then $\frac{a1}{a2}+\frac{a2}{a3}+\dots+\frac{an-1}{an}+\frac{an}{a1}$ is always $\geq n$ $\leq n$ $\leq n^{\frac{1}{2}}$ None of the above
Tesla!
asked
in
Set Theory & Algebra
Apr 4, 2017
by
Tesla!
854
views
isi2004
set-theory&algebra
number-theory
3
votes
4
answers
19
GATE2017 ME-2: GA-3
If $a$ and $b$ are integers and $a-b$ is even, which of the following must always be even? $ab$ $a^{2}+b^{2}+1$ $a^{2}+b+1$ $ab-b$
Arjun
asked
in
Quantitative Aptitude
Feb 26, 2017
by
Arjun
1.6k
views
gate2017-me-2
general-aptitude
quantitative-aptitude
number-theory
3
votes
2
answers
20
GATE2016 ME-2: GA-9
The binary operation $\square$ is defined as $a\square b = ab+(a+b),$ where $a$ and $b$ are any two real numbers. The value of the identity element of this operation, defined as the number $x$ such that $a\square x = a,$ for any $a$, is $0$ $1$ $2$ $10$
makhdoom ghaya
asked
in
Quantitative Aptitude
Jan 20, 2017
by
makhdoom ghaya
2.0k
views
gate2016-me-2
quantitative-aptitude
number-theory
easy
0
votes
1
answer
21
UGC NET CSE | June 2010 | Part 2 | Question: 9
What is decimal equivalent of BCD $11011.1100$? $22.0$ $22.2$ $20.2$ $21.2$
makhdoom ghaya
asked
in
Digital Logic
Sep 15, 2016
by
makhdoom ghaya
797
views
ugcnetcse-june2010-paper2
digital-logic
number-theory
6
votes
3
answers
22
ISI2016
Find the number of positive integers n for which $n^{2}+96$ is a perfect square.
abhi18459
asked
in
Set Theory & Algebra
May 9, 2016
by
abhi18459
1.2k
views
isi2016
set-theory&algebra
number-theory
numerical-answers
3
votes
3
answers
23
GATE2012 AE: GA-8
If a prime number on division by $4$ gives a remainder of $1,$ then that number can be expressed as sum of squares of two natural numbers sum of cubes of two natural numbers sum of square roots of two natural numbers sum of cube roots of two natural numbers
Akash Kanase
asked
in
Quantitative Aptitude
Feb 15, 2016
by
Akash Kanase
1.7k
views
gate2012-ae
number-theory
quantitative-aptitude
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